Privacy as Commodity: MFG-RegretNet for Large-Scale Privacy Trading in Federated Learning

2026-03-30

AI Summary

This work addresses two critical challenges in federated learning: privacy leakage from gradient inversion attacks and the lack of effective incentives for clients to contribute high-quality gradients. To tackle these issues, the paper introduces a novel privacy trading market by treating differential privacy budgets as tradable commodities. It proposes the MFG-RegretNet mechanism, which integrates mean-field game (MFG) theory with a differentiable auction framework (RegretNet) to efficiently compute a large-scale Bayesian Nash equilibrium while ensuring incentive compatibility and individual rationality. Experimental results on MNIST and CIFAR-10 demonstrate that the proposed approach significantly outperforms existing baselines in terms of auction revenue and social welfare, all while maintaining competitive model accuracy.

Abstract

Federated Learning (FL) has emerged as a prominent paradigm for privacy-preserving distributed machine learning, yet two fundamental challenges hinder its large-scale adoption. First, gradient inversion attacks can reconstruct sensitive training data from uploaded model updates, so privacy risk persists even when raw data remain local. Second, without adequate monetary compensation, rational clients have little incentive to contribute high-quality gradients, limiting participation at scale. To address these challenges, a privacy trading market is developed in which clients sell their differential privacy budgets as a commodity and receive explicit economic compensation for privacy sacrifice. This market is formalized as a Privacy Auction Game (PAG), and the existence of a Bayesian Nash Equilibrium is established under dominant-strategy incentive compatibility (DSIC), individual rationality (IR), and budget feasibility. To overcome the NP-hard, high-dimensional Nash Equilibrium computation at scale, \textit{MFG-RegretNet} is introduced as a deep-learning-based auction mechanism that combines mean-field game (MFG) approximation with differentiable mechanism design. The MFG reduction lowers per-round computational complexity from $\mathcal{O}(N^2 \log N)$ to $\mathcal{O}(N)$ while incurring only an $\mathcal{O}(N^{-1/2})$ equilibrium approximation gap. Extensive experiments on MNIST and CIFAR-10 demonstrate that MFG-RegretNet outperforms state-of-the-art baselines in incentive compatibility, auction revenue, and social welfare, while maintaining competitive downstream FL model accuracy.

Problem

• Federated Learning
• Privacy Trading
• Incentive Mechanism
• Differential Privacy
• Gradient Inversion Attacks

Innovation

• MFG-RegretNet
• privacy trading
• federated learning
• mean-field game
• differential privacy